I finally figured out that though a tool like WinRar shows that the embedded object is SFX zip volume, it actually is a MS-CFB (Compound file binary) file.

You can work with CFB files in the following ways:

Windows API: ole32.dll provides methods to read and write CFB files. I found this excellent article on this topic.

There are some useful resources on this page that refer to some open source options.

Bottom line, in order to work with office documents embedded in other office documents as embedded objects, are saved in MS-CFB format. Reading and writing to these files needs to be done outside of Open XML SDK, either using Win API or any other alternative.